A variable is a named memory address in which a value may be stored and mutated.
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Use the definition of a function. If, for any value of one variable, there is only a single possible value of the second variable, then the second variable is a function of the first variable. The second variable is often called the "dependent variable". If you can solve an equation explicitly for the dependent variable, then it is a function. If you can NOT solve it for a variable, it may or may not be a function - it turns out that some equations are hard or impossible to solve explicitly for one of the variables.
For an algebraic function in one variable, as many as the highest power of the variable.
Dependent variable
You cannot.
A function that has a variable under a radical sign.